The common ratio in a geometric series is $4$ and the first term is $3$. Find the sum of the first $8$ terms in the series.
Explanation: This formula gives the sum ${S_n}$ of the first $ n$ terms in the geometric series where the first term is $ a$ and the common ratio is $C r$ : ${S_n}=\dfrac{ a(1-C r^{ n})}{1-C r}$ We are given the values for $ n$, $ a$, and $C r$. All we need to do is plug them in the formula. We are given that ${n=8}$, ${a=3}$, and $C{r=4}$ : ${S_n}=\dfrac{ 3(1-C 4^{{8}})}{1-C 4}$ Evaluating the expression in the calculator, we get that $S_n=65{,}535$. In conclusion, the sum of the first $8$ terms in the series is $65{,}535$.